Then, to illustrate the effectiveness of our proposed set inversion algorithm for continuous-time systems, we consider observations/measurements similar to [1]}, as follows. In the \(X\) –\(Y\)  plane, two known points, denoted as \((s_{x_i} , s_{y_i})\)  \((i = 1, 2)\) , are chosen as markers/landmarks. Then, the distance from the robot's planar Cartesian coordinates \((s_{x,t}, s_{y,t})\)  to each marker \((s_{x_i}, s_{y_i})\)  can be expressed as \(d_{i,t}=\sqrt{(s_{x_i}-s_{x,t})^2+(s_{y_i}-s_{y,t})^2}\) . Furthermore, the azimuth \(\phi _{i,t}\)  at time \(t\)  can be related to the current system state variables \(s_{x,t}, s_{y,t}\)  and \(\theta _t\)  as \(\phi _{i,t}=\theta _t-\arctan (\frac{s_{y_i}-s_{y,t}}{s_{x_i}-s_{x,t}})\) . Treating both the distance \(d_{i,t}\)  and the azimuth \(\phi _{i,t}\)  as the measurements, as well as considering measurement disturbances /noise \(v_t\) , the  nonsmooth, nonlinear observation/measurement equation can be written as:
\(y_t=[d_{1,t} \ \phi _{1,t} \ d_{2,t} \ \phi _{2,t}]^\top +v_t,\) 
